A brief review of the Fermi-Pasta-Ulam (FPU) paradox is given, together with its suggested resolutions and its relation to other physical problems. We focus on the ideas and concepts that have become the core of modern nonlinear mechanics, in their historical perspective. Starting from the first numerical results of FPU, both theoretical and numerical findings are discussed in close connection with the problems of ergodicity, integrability, chaos and stability of motion. New directions related to the Bose-Einstein condensation and quantum systems of interacting Boseparticles are also considered.

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We present a rigorous analysis of the phenomenon of decoherence for general N −level systems coupled to reservoirs. The latter are described by free massless bosonic fields. We apply our general results to the specific cases of the qubit and the quantum register. We compare our results with the explicitly solvable case of systems whose interaction with the environment does not allow for energy exchange (non-demolition, or energy conserving interactions). We suggest a new approach which applies to a wide variety of systems which are not explicitly solvable.

We consider a qubit interacting with its environment and continuously monitored by a detector represented by a point contact. Bloch-type equations describing the entire system of the qubit, the environment and the detector are derived. Using these equations we evaluate the detector current and its noise spectrum in terms of the decoherence and relaxation rates of the qubit. Simple expressions are obtained that show how these quantities can be accurately measured. We demonstrate that due to interaction with the environment, the measurement can never localize a qubit even for infinite decoherence rate. : 73.50.-h, 73.23.-b, 03.65.X. PACSAn account of decoherence and relaxation in quantum evolution of a two-level system (qubit), interacting with an environment and a measurement device, has become a problem of crucial importance in quantum computing. Numerous publications have appeared on this subject dealing with interactions either with a measurement device (detector) [1][2][3] or with the environment (a thermal bath) [4,5]. Generally, the simultaneous influence of an environment and a detector on a qubit is very important for understanding qubit measurements because the environment and the detector act on the qubit in different ways. For instance, the environment at zero temperature relaxes the qubit to its ground state. As a result the qubit finally appears in a pure state, even though it was initially in a statistical mixture. On the other hand, the measurement device puts the qubit in a statistical mixture, even if it was initially in a pure state.One of the most striking measurement effects in which the role of relaxation has not been investigated is the socalled Zeno paradox [6]. It consists of total freezing of a qubit in the limit of continuous measurement. Usually, it is associated with the projection postulate in the theory of quantum measurements. Indeed, it follows from the Schrödinger equation that the probability of a quantum transition from an initially occupied state of a qubit is P (∆t) = a(∆t) 2 , where a is a factor which depends on the system [6]. If we assume that ∆t is the measurement time which determines the timescale on which the system is projected into the initial state, then after N successive measurements the probability of finding the qubit in its initial state, at time t = N ∆t, is P (t) = [1−a(∆t) 2 ] (t/∆t) . Thus P (t) → 1 for ∆t → 0, N → ∞ and t=const. Including the environment into the Schrödinger equation for the entire system one would expect from the above arguments that the relaxation processes could only affect the coefficient a, but cannot destroy the qubit localization in the limit of ∆t → 0.This conclusion, however, is not correct. We demonstrate in this Letter that any weak relaxation delocalizes the qubit even in the limit of continuous measurement. It is shown by using new Bloch-type quantum rate equations for the description of a qubit interacting with a detector and its environment. These rate equations are derived from the microscopic Schrödinger equation for the e...

We investigate the role of long-lasting quantum coherence in the efficiency of energy transport at room temperature in Fenna-Matthews-Olson photosynthetic complexes. The excitation energy transfer due to the coupling of the light harvesting complex to the reaction center ("sink") is analyzed using an effective non-Hermitian Hamiltonian. We show that, as the coupling to the reaction center is varied, maximal efficiency in energy transport is achieved in the vicinity of the superradiance transition, characterized by a segregation of the imaginary parts of the eigenvalues of the effective non-Hermitian Hamiltonian. Our results demonstrate that the presence of the sink (which provides a quasi-continuum in the energy spectrum) is the dominant effect in the energy transfer which takes place even in absence of a thermal bath. This approach allows one to study the effects of finite temperature and the effects of any coupling scheme to the reaction center. Moreover, taking into account a realistic electric dipole interaction, we show that the optimal distance from the reaction center to the Fenna-Matthews-Olson system occurs at the superradiance transition, and we show that this is consistent with available experimental data.